Besides people who don't get this reference, of course
I hate people who post ‘gamer logic’ pictures. Quite a bit. “Hey, did you know the police will give up on chasing you after 50 feet? Lol, not like real life at all” “Falls into hay off Empire State Building. Survives”. Shut up. No one cares. Games are about fun, not realism. Any game that sacrifices fun for being realistic has failed as entertainment, in my mind. Take for instance, Receiver: a first person shooter where you have to reload in a real fashion. As a thought experiment, it is really fun. PvP in the game would be a wonderful fustercluck. The novelty is interesting, but the actual gameplay is less entertaining, than say, pressing R then continuing to shoot stuff. I think FarCry handled it very well, but on the fly, brutal self surgeries, but still keeping pace.
Whoa dude, you are soooooo right! I can never play Mario the same way again! But seriously, headbutt a bullet.
So why do I bring all this up? Well, I have one complaint that actually does drive me crazy about videogames. It’s like some weird kind of fear. And that is that I am almost never standing on solid ground. Ever. I am playing a game in a papercraft diorama of what a real world situation might look like.
For anyone who has played Dark Souls on PC, you may be familiar with the DSFix mod. One aspect is that you can unlock the frame rate which comes with the ominous message that you ‘may’ fall through the floor on occasion. And that is genuinely what happens. Instead of sliding down a ladder and having your feet touch ground, your slide shreds the paper flood beneath you as you descend into the dark void.
Thanks to the Game Grumps I now know how flimsy the world of Skyrim is. Everything in the game is paper thin. The floors. The walls. Mountains. Stairs. Other humans. There are no guts...no brains...just a shell with facial muscles, eyes, and teeth. Some kind of walking talking flesh heap. But even worse, these systems allow the player to abuse these systems by the use of a bowl...you can literally use a bowl to walk through walls, falling through the abyss and seeing the darkness of the world outside of your doll house. It’s just...creepy.
Almost every game where you are playing in a 3D environment has the same situation. You can often tell this just by moving the camera so that it clips through the one dimensional layer. Behind every brick is just another flat surface. No dirt. No minerals. No fossils. Just...nothing. Its like walking on ice.
Oh yeah, thats the good stuff.
So this explains why it is so comforting to me when the games let me know what is around me. Minecraft is a fantastic example. Every single structure is actually made up of blocks. You start on grass, but you can see the feet of dirt, stone, and eventually bedrock beneath you, and even if you find a gap in the bedrock, you just fall into the core of the earth and die. It almost makes sense in that regard. Terraria uses the same system, so it is also nice to see that other people share my odd phobia. As far as the people, there have been some fairly good advances in this as well! Most zombie games at least recognize that humans are made up of 4 limbs, a torso, and a head with a brain. Sniper Elite even goes a step further and fills in the remaining organs and bones, and even shows how people die as your bullets rip through their organs. The entry and exit wounds leave something to be desired, but remember what I was saying above about reality? Bloody gaping wounds followed by muffled screaming? Not fun. There are also the new Mortal Kombat games which used the XRay system to show the damage that was done. Was it exclusive to a QTE? Sure. But it helped to...flesh out the world.
I was musing on this a bit, and I realized that only modern games have this problem. See, back in the good old days of the NES and SNES, a few bricks were reserved for the ground. Mario had a brick and a half beneath his feet. Even if, for some reason, he jumped super hard, he would still have a lot of brick to go through. Even Simon Belmont had a good block beneath his feet most of the time.
I know I’m crazy, but does anybody else share this kind of paranoia?
When was the last time that you snap bought a game, sight unseen. Sure, some people buy games day 1 after tons of press release, or after enjoying the previous game in the series, but a game that just sort of stumbles out there, well...odd things can happen. Sometimes, they are beautiful, and sometimes they are hideous decisions. Being a PC gamer, I can resist the temptation of almost any game on the basis that I know it will be for sale in the near future, and I have an incredible backlog to play through. That did not stop me when I saw “Sniper Elite Nazi Zombie Army”. I had played Sniper Elite V2, and found it….lacking, to say the least. But seeing a combination of Nazis AND Zombies used so blatantly, with pentagrams, and a B movie horror flair behind it? That was a game that I had to pick up. Knowing nothing of what I was getting into, I put the money down on that game. It turned out to be a Sharknado/Snakes on a Plane experience...you pretty much pay to say the name for the next month or so, but it is enjoyable while it lasts. Delivers what it promises. Not to get too far off topic, the first game was actually incredible, in my opinion. It took the mechanics of the first game and refined them in every single way, almost to a comical fault. The joy of playing a sniper is being able to shoot people’s heads, and what better target than one that can barely walk towards you? SEV2 (acronyms, begin!) gave you tools to set traps, but you had to have the foresight of knowing where to place them. SENZA gave you an improv situation - you could guess what will and will not be critical. Secondary weapons had purpose! Running like an idiot and wasting your breath was important! It was really, genuinely, fun. From a mindless face exploding simulator point of view, it was literally all I could ask for.
Then I saw that the sequel was coming out. And I made another snap purchase.
So after singing praises of the first game, lets talk about the core of the game in 2. Yet again, you have hordes of the undead coming to attack you at a very slow pace. The core mechanics had absolutely no changes, which felt like a bit of a missed opportunity. As much as the first game demonstrated how the mechanics could transcend stealth into horror/tension, it would have been great to see a progression of the mechanics against zombies. Some new weapons, tricks, and traps would have gone a long way to make things feel ‘fresh’ after the 10,000th corpse. But overall, the gameplay largely remains the same, and is still incredibly satisfying to shoot zombies in the face. It harkens back to the days of Serious Sam and DOOM, where positioning is more important than twitch reflexes, but with the twist that you have to remain cool and collected enough to land headshots.
So lets talk about the changes. First, the game commits a cardinal sin about halfway through and introduces stationary turrets. Both SENZA and SENZA2 have optional 4 player coop, but the turrets really begin to push the boundary of how optional it is. Several sections are clearly designed to have at least 2 people (one guarding left with a turret, the other guarding right), and having another 2 to defend your backs would be wonderful. There was one section that painfully brought this up, and made the game feel like more luck than skill, and you had to predict which side a special infected would come from. They are a good addition in theory - breaking up the careful, planned sniping with mashing down the trigger can be both refreshing and cathartic, but often with a single player, it just fell flat.
So lets talk about the special infected! All the gang are back from the last time, and are still as fun as ever. Besides your standard zombie, you also get skeletons - who now shamble out of walls or burst out of mannequins, both of which are pretty dang creepy. Then you have suicide zombies, akin to the guys with bombs for hands from Serious Sam, but less obnoxious. There are counter snipers, who make great use of the bullet drop physics. Then there are the machine gun zombies, hulking titans who can shoot back, and require several rounds to the face to take down. Finally, the occult commander makes a return appearance, much to my dismay. It is worth noting that the commander and the machine gun zombie both faced some nerfs between the series, which was more than welcome for the former.
Then there are the new boys, and you know what? They nailed it here. There is a zombie who can explode, converting nearby zombies into flaming zombies who run directly at you. He is annoying as hell to fight, but offers a new, fresh challenge. Then there are the summoners. They do what you would expect, really. The challenge is that they can only be killed with a headshot, and they move their heads around quite a bit. It offers a nice tension to have to get a headshot amidst an ever growing horde of the undead. Later, they start placing them in rather difficult places to account for, and it really winds up being fun.
The atmosphere remains more or less the same as the first game, but they did add in a few unsettling moments into the game. A few points really reminded me of the FEAR series. Wait, scratch that, just FEAR and Extraction Point. You know...the good ones. It is amusing having played SEV2 seeing how often they recycled the assets of the levels to change them around to fit the zombie theme. Sometimes they are well hidden, other times they are wholesale rip offs, but overall it still has more charm than budget. I really would like to see more developers taking note of how they are doing this for future projects similar to SENZA or Blood Dragon. High in charm, and I assume low in work, as models already existed. With all that said, however, the game seems to have lost some of the charm. I can’t put my finger on it, but something about it just doesn’t feel like the same bad B movie feeling. It plays it too straight or something.
So, at the end of the day, it really is more of the same from the first game. If you liked that, I would say that you would enjoy most of the sequel. If the first game just wasn’t your jam though, this offers absolutely nothing new or redeeming. And if you are on the fence...well, wait until it is on sale, grab some friends, grab some beers, and make a night of it. There are only 5 levels, and each level is only about 40 minutes long on average, so it is a pretty short romp. There are collectibles, but I never find those rewarding. After beating the game solo, I do look back on it fondly, and if anyone was getting a group together to four man this bad boy, I would be first to reinstall it.
OH! Also! I recorded my entire playthrough of the series! First video for SENZA is here:
As is the case with the previous blogs, I ran into a question that I had to answer by using spreadsheets, math, and prayer. This time around, the question came up from the wonderful game Path of Exile. In Path, you have 4 damage reduction systems: armor, block, dodge, and evasion. Armor and evasion come from the gear that you are wearing, block comes from your choice of shield, and dodge comes from passive skills. Block, dodge, and evasion all negate the attack you are taking, whereas armor will reduce the damage by a set amount, based on math (more on that later). Now because I didn’t feel like messing around with 4 variables, and because only 2 come up very often with every class, I wanted to figure out:
What is the best combination of block and evasion?
Now, obviously, 100% of both would be the best, so it becomes rather important to phrase the question. Basically, there is armor that has about both stats in about half the amount of ‘dedicated’ gear. So would you be better taking 50/50? Or maybe 70/30? Or just not worrying about one at all? My mental roadblock with all this was that it seemed like there might be a sweet spot of reducting the damage that you don’t take.
So lets talk about the math required to figure out the first part of this challenege. We know that evasion has a chance to proc each time, so it will fall into normal distribution, whereas armor is conistent. Now as you SHOULD REMEMBER FROM THE LAST TIME, the difference is negligible in the long run, but is rather swingy in the short run...in theory. Path actually does use psuedo random distribution (a method by which they force the ability to proc after X events, in a way that still results in approximately the same odds). For the purpose of the math I’m doing though, this doesn’t matter. In fact, I can treat block and evasion as exactly the same! The reasoning is that if you took 100 attacks at 100 damage with 50 of either armor or evasion, the armor would block 50 from each, for a total of 5000 blocked, and the EV for evasion would be ½ of all attacks, for 50 blocked attacks by 100 damage for, you guessed it, 5000 damage. So by putting 10% block to 90% evasion, and increasing/decreasing by 10, I get something like y=x^-2 : an inverse parabola.
Probably about the 3rd saddest time in my life to see a parabola, really
Oh. Well. Looks like this week is pretty short, huh? Assuming each attack coming at you hits for 100, that means that the 50/50 block gives .5*.5, or 25% total damage received. 90 by 10 gives 9%. So really, there is no sweet spot. It is always better to focus on one or the other. Really obvious in hindsight.
In a vaccuum at least. In reality, it gets a little bit more complicated than that, but not by a whole lot. The assumption made throughout that process is that you have access to whatever gear you would need, and the resources to get it all - more often than not, this is not the case. So then we have to understand the value that we are getting from each piece of armor, and in order to get that, we need to know how many pieces, and in order to get that, we have to build a model! Yay!
So lets talk about how these mechanics scale. We would need a curve that start at 0, and infinitely scales at either 100 or 90 - I still haven’t figured exactly how Path does this, as the math that the wiki provides does one thing, but says the other. Path has a 90% cap on the damage you can reduce, but the theoretical amount you can block actually scales to 100%. For reference, the equation I found is “Armour / ( Armour + (12 * Damage) )” So as armor increases, it grows ever closer to being 1, but even at millions of armor, you still take a teensy bit of damage. Evasion’s calculation is actually a lot more complicated, because it uses an enemy’s accuracy stat, so I am going to again make a large, sweeping assumption, and say that evasion scales the exact same way that armor does. Now, you can rearrange the above equation to get Total Armor = (12*Damage*Desired Reduction%)/(1-Desired reduction%), which lets us figure out how many units we would need for any given reduction.
Diminishing returns apply both to how much armor you have, and how much you pay attention to me
So applying this formula to our ratios gives 134 armor required to get to the 10% threshold, and 10800 to get to the 90% threshold, if facing 100 damage. That is an 8,000% increase to get a 900% gain! Hooray! Math! So the same thing applies for evasion. This means that in order to get the 90/10 split, we would need to have a total of 10,934 points. However, in order to get to the 50/50, we only need 2400 points (as 1200 is the 50% point for both). So, we would have to increase our total stats 4 times over to get 2.7 times the gain. Ok, cool. Now we are getting somewhere!
This means that each piece of armor is contributing less ans less as we add more and more. Specifically, our best case example has each piece of armor protecting us from .0313 damage, or 32 units to block 1 damage. The 90/10 example, however, is .0083 or 120 untis to block a single point of damage, supporting our previous 4 to 1 numbers. Neat! So for right now, it looks like it is all up to context right?
Its been too long since I have thought of this scene, or this movie. Needed to be fixed. By math.
So far, I assumed you had a tradeoff between armor and evasion, but what if we lifted that restriction. Well, you wind up with the 60/60 build, which offers 84% damage reduction. This happens to be the same as the 80/20 split, however it does it with 1,500 (!) less units of armor, with an efficiency per unit of .0233, or 42.86 (comparable to 70/30)! Whoa! Then we can step it up to 70/70, which gives 91% (the same as the 90/10 split), for 5,600 units (efficiency of .0163, or 61.54 units per damage reduced). Then we have the 80/80, offering up a hearty 96% reduction at .01 per unit...which is both more reduction than the 90/10, and less cost!
Now unfortunately, I am writing this up late and don’t have access to Excel (or the effort to boot up my work computer to get it), just Google’s charts, so I can’t do a proper regression to figure out all the math for it, so I cant tell you if it is some super cool exponential curve, or something like that, but what I can tell you, for sure, is that it is 100% better to scale your stats equally is possible. Because the systems are set up the way that they are, you are losing value the more armor that you take. However, by abusing the relationships between the two curves, you can make significant gains by balancing your stats. In context, this may be tricky - A vendor may not have a 700/700 armor, only 500/500 or 1000/0. Now, can you imagine what this would have looked like if we had included another system, such as blocking or dodging? What a headache!
In addition, the games methods may not match what this math is exactly...for instance, Path starts each character off with a base 5% dodge meaning that my treating dodge and block as the same is a little bit faulty, plus the enemy accuracy plays a large part into how the mechanic works. Further clean up and asterisks, I did use 100 for the base damage of an attack, and using any other number changes the exact numbers that will come up. However, the scaling is set up in a way where the damage to armor required ratio scales linearly - so the armor required to soak 90% of 300 damage is exactly 3 times the armor required to soak 100 damage.
Other than that though, there you have it! The answer to a question, as solved by math! And your professor said it didn’t have any real world applications.
I was talking out loud to myself while playing a videogame, and I had an interesting question come up, one which could only be solved by using the worst of all demons: Math. So let me phrase the situation for you guys...You are playing an RPG. At the beginning of the game (or whenever, really, but my numbers use a level 0 assumption), you can take a perk that offers you an extra 10% on every single experience granting transactions. Is it worthwhile to take this perk?
Now, the gut feeling towards this changes day to day. Clearly, the earlier that you take the perk, the more effect that it has, meaning you should take it is as early on as possible. Second, that’s an extra ten percent, baby! One tenth of each level is free! However, what exactly does that imply...that means that I will not have a significant experience advantage over anyone who didn’t take the perk until level 11 - they will still be at ten. This continues for each ten levels. At level 20, I have only managed to eke out an extra 2 levels over my theoretical friend. So would I have been better off to have taken another skill in its place?
Both of those arguments are easy enough to conceptualize, but the benefit that you are getting from either decision is actually pretty hard to quantify without using some math. The reason? We all know that RPGs are drip fed - the difference between level 1 and 2 is nowhere close to the difference between 20 and 22. This is largely in part to the way that experience is curved out. Because of this, I couldn’t come up with a satisfactory answer and I had to do some math. To start with, I had to design an RPG Exp curve, along with average monster exp. Having no background in game design, this is something that has always fascinated me...how do they know how much gold and exp to hand out in any given area, but still maintain balance? In my mind, there was some master spreadsheet kept in the back that told them, similar to an actuary table. In reality though, calculating this is quite easy! So I wanted to dedicate a lot of space to how I set up this example…
Or I could just...you know...plagiarize one. But where's the fun in that?
I started messing around with each level being exponentially far away from the previous level, but wow, that gets out of control quickly! I have never seen an exp bar go into scientific notation, so I clearly had to use a different approach.
I decided that first, the RPG system is a drip feed so the time it takes to reach a level should increase at each level. After messing around with some models for a bit, I discovered that the time to level is probably the first factor that you want to decide on. I figured that if you added an extra 15 minutes to each level, that would probably be enough to keep things balanced - 15 minutes to level 1, 30 to level 2, etc.
Next, you have to know the average amount of experience you are giving out per level. I decided to make an assumption that the exp per monster would also increase in a linear fashion - 50 at the first level, 100 at level 2, and 150 at level 3. These numbers could be anything and it should all still work out. Next, I made yet another assumption that each fight would take exactly one minute. I guess you could replace the minutes with encounters and it would still be the same, but for some reason I was hellbent on using fractions of hours in Excel, so...it stays as minutes.
So what does that let you do? Well, now you can take the total experience per encounter, and multiply it by the encounters to level up! This gives the experience gap between levels! In our case, it takes 750 to reach level 1, an additional 3000 to reach level 2, then 6750, and so on (spoilers if you figure out what ‘and so on’ means here, I suppose!). Taking the cumulative values of all of these gave me an exp curve that starts at 750 for level one, and ends at 7 million for level 30, after a hefty 116.25 hour journey!
Now here is where something happened that blew my mind...I had created an RPG curve that I was satisfied with, and wanted to know how it was modeled. I took the data for cumulative experience and put it on a plot, tried some regressions, and nothing quite matched. It looked close on one or two, but the fit wasn’t perfect. Maybe it just wasn’t that mathematical. Then, because I was bored/wanted to be thorough, I put a regression on the experience between the two levels, and discovered that it fit a 2nd order power regression perfectly. Not ‘really really well’, not ‘pretty close’, but 100% perfection. Then I thought about what that meant. If I had the value between two points on a chart….and it was represented as aX^2+bx+c….then that is the integral of the experience curve! And sure enough, the experience curve comes up as a 3rd power regression, with a 100% fit, whose derivative gives the fit of the exp between charts (+ c, naturally)! Holy crap! Thats awesome! That also means that I can take the derivative of the experience between levels to get….something….related to the experience...I didn’t actually figure out what that would give me as it has been a while since I have performed a calculus, much less on a real world example.
Pretty much 'mfw'
After this, it becomes pretty simple to figure out how the scaling works. Just slap on an extra 10% to the exp per fight, and do the division. And what do we get? Well, the initial assumption actually holds true...the player with the extra 10 percent hits level 22 at 57.5 hours of play, at which time the player without the perk is just barely level 20. The comparison for 10 and 11 is 15 and 13.75, so it isn’t quite a clean cutoff, but the marginal gains are clearly there. So it really doesn’t seem like much, does it? Maybe you could take a perk that gives +20% damage which pays off at every single level instead of getting an extra level every 10 levels…
...Except the way that the levels are curved out showed me something different. In order to reach max level, it takes the player with the perk 105 hours, and the player without 116 hours. In fact, it is taking the second player an average of half an hour less past level 20 to level up. So it isn’t what you are gaining in levels over another player, but perhaps the time you are gaining back from the game. If a perk said ‘save you ten hours of leveling’, would that be worth it?
But then this is where things get extraordinarily more interesting (or more boring, but if you think that and you made it this far...uh...thanks?) Because of the way that the experience scales, you save less time in the early levels as opposed to the later levels. From levels 1 to 7, you only save half an hour by taking that perk. From 23-30, you would save 5 hours, which is to say 10 times more time! So this is where the final wrinkle of this puzzle is introduced..in fact, you do not get more value by taking the perk early, as logic might dictate. While it is true that having it wouldn’t be a bad move at early levels, its effects are most pronounced in the late game. This is again because of how the experience distribution curve is calculated - for lower levels, the difference between 1.1 and 1.0 multiplied by x^3 makes less of a difference, but for higher levels, it suddenly becomes a much larger gap.
While discussing this with one of my coworkers, he actually brought up an excellent point, which I had not initially considered when writing this, but was actually the very thing that brought it to my mind: In some RPGs, traditionally the western RPG, enemies scale with the player! This means that you are actually inflating the difficulty at a rate which it should not be inflated, and losing a perk in the progress! At level 10, you only have 9 perks working for you if you took the extra level, making you 1 perk behind the slower player! So all of the sudden you are trading a decrease in time for an increase in difficulty! Oh no! The example that brought this to mind was actually Dead Island: as far as I could tell, the zombies 'leveled' with you by gaining new abilities, such as increased mobility, better climbing, larger numbers, things like that. So I constantly felt that, while I was better off in total exp, I was actually playing a much harder game than I should have. And we call this the Ayn Rand paradox of game design, wherein the player who made the 'smart' decision to have more exp is punished by the unflinching machine of poor game design.
Now obviously, this is just an example of what an experience curve could look like, and most of the numbers were chosen by an arbitrary method, but the principles still apply. So what can we draw as a conclusion? Basically, taking the perk early isn’t actually that important...in fact, you get more value from it the later that you take it, on a per level basis. As long as the early grind isn’t that bad, it is totally worth holding off. And as far as being worth it in general, it comes down to a matter of the value of your time. If the game is something like Final Fantasy where you are expected to grind out between levels, it is probably going to be worth it. But if the game is something like Fallout where having levels is nice, but not required? Maybe just enjoy the sights. Certainly, dont waste your perk to make the game harder - most games have a slider for that! In any event, you should now be more prepared each time you face that decision!
So a while ago, I was browsing some site on the internet, probably pornagrophy of some sort. I guess I must have become side tracked, because I encountered a hypothetical videogame situation: after slaying 1000 hyperdemons, you have been given a choice of rewards. You can either select the Red Sword, or the Blue Sword. The red and blue sword both deal the same amount of damage, but here is the catch: the Red sword hits 100% of the time, Blue hits 50% of the time but can attack twice as often. Which sword do you take, and why?
Now, obviously, this situation has 3 choices:
A. The Nihilist Approach - “it doesn’t matter which one I take”
This seems like it should be obvious, right? After all, you just have to do some basic math in order to come to this conclusion. Lets say both swords do five damage. In 100 attacks with the red sword, I will do 500 damage, and with the blue sword I get half of 200 attacks by five, for - wait for it - 500 damage. So, as long as its better than my other gear, my choice, much like every choice in life, has no meaningful impact.
B. Team Red- “I have terrible luck”
Yes, you nihilist, on paper, given a large amount of trials, the two will be equal. But this sword relies on a RNG when it decides to hit. This means that in theory I could miss more than I hit with the blue sword, because this stupid game is rigged! If I pick the red sword, I am guaranteed my 500 damage. The blue sword is eventually going to fail me if I take it, it is only a matter of time.
C. Team Blue- - “Maaaaaaybe”
There are a lot of maybes in the game. Maybe an enemy dodges. Maybe I get lucky. Maybe I crit! Maybe I can buff the sword! (For the purposes of discussion, neither of these are true. Sorry.) Bummer...well, at any rate, maybe every once in a while I can get really lucky and do some serious damage.
D. None of the Above
Wait...what? How did you….nevermind. You know what? You have to re-choose. House rules.
So which option would you end up picking? From what I saw, it was about 40/50/10 between A B and C. What would I pick? Well, the answer depends a lot on two different things: Statistics and context. Lets look at the former first.
If the odds of the blue sword hitting are forced to be 50%, then anyone who picked A would be correct in that it doesn’t make a difference. But if we assume that the RNG behind the scenes runs an independent check before the next number, that means that a series of coin flips will be normally distributed. However, because a coin only has 2 outputs, a graph of that looks pretty darn lame:
So lame, in fact, I'm not even giving it real data
Where it gets interesting though, is when you perform multiple trials of multiple coin flips. So, for example, lets say you expected to be able to survive 100 turns against a monster. That means that you get 100 coin flips throughout the course of the battle. And you could say that you will fight, for the purpose of example, 500 encounters. Some encounters will result in more hits landing, some will result in less hits landing. But what is neat, is the pattern that these observations create. Because all the coin flips were independent, we expect them to fall in to a normal distribution, along a bell curve.
Oh sweet Jesus, normal distribution.
This is where things get amazing! Because bell curves have already been analyzed to death, I don’t have to do any dirty work, and can just spit out numbers from any statistics textbook and/or website! The average for this curve, based off 100 coin flips, is going to be at the center with a value of 50. The chart can be broken down by standard deviations to figure out what percent of the area is made up by what values. If we know the standard deviation of the data, we can figure out how much area is under each section of the curve, and so, how unlikely it would be to see that value come up. As it turns out, for 100 random trials the standard deviation would be somewhere in the ballpark of 5. For the first 5 in either direction from the median, we cover 34% of the area under the curve, because math. Neat stuff, right? (You can say no...I don't mind...but I think its neat)
So how does this affect our two swords? Well, it means that there is only a 32% chance for us to be outside of 1 standard deviation of hits, so either above 55 and below 45. It also means that there is only a .26% chance of being outside of the 45 to 65 range. In fact, out of 10,000 simulated trials done in excel, only 360 were outside of +/- 10 from the average, as we would expect with the math.
So with that somewhat explained, how does it apply to the situation at hand? First, you would need to know how many rounds you have against each monster, and how much health they have. Then, you have to figure out your level of risk. So assuming that we are only fighting monsters that kill us at exactly at our previously selected arbitrary limit of 100 turns. If they have 500 health, in the long run, it doesn’t matter which sword we pick... but half the time, we will probably die. Not looking great for the blue sword. It can take out enemies with 45 health 85% of the time, though, but that is nothing compared to Red’s 100% win rate!
...but what happens if a monster has 505 health? Red’s win rate drops to 0%, while Blue’s is just barely under 50 percent. Suddenly, we made up a ton of ground. Or if we have to deal the same damage within a shorter time limit? Again, Red suddenly has no choice but to resign to never beat the game without better gear, whereas Blue can suddenly begin to shine. In fact, if we had infinite time, we could kill a monster that has a full 1000 health! It would be like winning the lottery while getting eaten by a rabid shark that was just struck by lightning, but theoretically...it could happen!
Now, you won’t always get 100 rounds against your opponent, which affects some of these numbers. As the number of rounds increase, the effect of the variance decreases thanks to the Law of Large Numbers. This means that as the number of turns decrease, the variability is more pronounced. So lets look at what happens with ten turns instead of 100. The average damage is still where we would expect it to be at 5, but the standard deviation changes to be 1.5. This means that our 68% is now within 3.5 to 6.5, and our .26% is now at .5 to 9.5. Suddenly, it doesn’t look like quite the best option yet.
Now here is one final thing to consider about the two swords, and is something that I have yet to mentally reconcile, to be honest. If you have 2 attacks at 50% to hit, the expected result would be that, on average, 1 attack hits each time. But consider this: each turn has 4 possible outcomes, each with equal odds of happening: both miss, only the first hits, only the second hits, or both hits. 3 of the 4 outcomes are equal to or better than the Red sword, so you have 3:1 odds of Blue being the same or better!
But ultimately, math cannot make this decision. In the end, you have to go with your gut as to what ‘feels’ the best, and a lot is to be said for the context. However, I hope that this has helped in your consideration when encountering similar scenarios. Or at least you’ll have an ethos.
When I was young, I played a lot of Battletoads, and somewhere along the line my young brain mixed up The Beach Boys with Battletoads. Seeing some weird bearded dude instead of a anthropomorphic frog just seems weird to me. Anyway! Picking up where others have laid it down, I wanted to get some good vibrations going through here. Also, googling 'good vibrations' might not be safe for work. Word of warning. Lets get started!
1.) Sniper Elite Nazi Zombie Army 2
The original Sniper Elite was one of my favorite little unexpected treats. It was like driving down the road and seeing a hole in the wall place called “Ted’s Smokeshack”, and ordering the heart attack express only to find that it didn’t make you sick, and also wasn’t half bad. I am almost ashamed to admit that I purchased the game on name alone, but it turned out to be rather enjoyable. It had a super campy soundtrack, plot, and well, everything. The really odd thing was that it elevated the mechanics of the original game into something more. A lot of features in the first were redundant or just useless - why would I need to plant and shoot dynamite as a sniper?
With the sequel, I figure that they probably will miss more than they hit, but hopes are still high. They need to fix the balance that absolutely didn’t exist in the first (more ammo is better ammo). The levels all lasted a little bit longer than I would have liked, and there were only five of them, so maybe doubling the level count and halving the length this time around.
But overall, it was a game that you couldn’t go wrong with. It was sniping at its finest without any of the stealth that made the original release so cumbersome. It plays up the blood and gore and camp or the game instead of trying to have some serious plot about subterfuge and missiles. It lets you shoot zombified testicles in slow motion. And its cheap. What more can a man ask for?
2.) Deadly Premonition PC Release
Speaking of budget games...Deadly Premonition exceeded my every expectation when it released on the 360. A super budget game, mostly marketed for its quirky sense of humor, odd cast of characters, and seemingly terrible acting and non sequiturs. Playing through the game though was an incredibly interesting experience. It dabbled in the world on the strange, but found itself often rooted in a reality that many games miss. It has odd ‘easter eggs’ thrown in the entire game that tie everything together in a way that no one would expect. It has several scenes that are some of the most emotionally gripping I have seen in recent years.
And now it is coming to PC! When I beat the game however long it came out ago - probably about two years - I knew that it was a ‘one of’ kind of game. The skydiving, eel eating, college streaking, kind of experience - you do it to say that you did it, and that should be enough. However, I found myself going back to Nier (the game that I played immediately afterwards), and enjoying that quite a bit more the second time around, so I am excited to go back through the town. Like I said before, knowing how everything ties out means that all the small clues left behind can be traced back.
Plus, I know how the mechanics work, and I feel no guilt playing on easy. Fun story from the first time around on the game: I didn’t know what the cigarettes did, and learned that you can use them to advance time. So I sat outside of my car and lit up a cigarette. After a few short seconds, a cutscene played. The skies turned red. A dog, 8 feet tall, barking, with saliva soaked jowls started to leap at me. I thought this was an anti smoking PSA until I realized the game had a ‘curfew’. Set me straight, tell you what.
Plus, this comes out about the same time as SENZA2:EB, so its going to be a fantastic Halloween!
3.) Dark Souls TWO
Oh my god guys. I love Dark Souls. If I were to make a list of top ten games of this generation, Dark Souls would easily make the list. Not sure on ordering. Demons Souls was hyped up beyond belief for me, mostly because I didn’t have a PS3. It sounded like a really cool concept, with an incredibly challenge that I wanted to sink my teeth into. When the sequel came out for the 360, I knew what had to be done. And I absolutely hated it. No paths, unpredictable traps, blatantly impossible sections, and obfuscation of essential mechanics. It wasn’t hard, it was crap. Each rage quit had me coming back, guide in hand, to tackle the next section though. I was good enough to beat it, and with my own rules. I didn’t want to use any noob play styles, so I swore off the FDS for my first playthrough. I went with full Havels and the black knight’s polearm. After 36 hours of grinding, torture, and cussing, I had emerged victorious. Then something strange happened.
I started it up again. I didn’t try the magic. Then I had to try the bows. Then the miracles. Then an int/dex build. The ideas just kept on snowballing, and challenges started to appear. The game, at its core, is possible to beat with any of the equipment. The greatest challenge is learning how to think while playing it. After 200 hours, I felt safe to close the chapter on the game. Until I could buy the DLC on PC for 7 dollars. This was my chance for redemption. If I could beat the DLC blind, I would truly consider myself a master. And I did. Easily. Now with 300 hours under my belt in the game, I am more than ready for the sequel.
What new challenges await? What tricks, what secrets, what bosses, what magic? Which invaders, which weapons, which unexpected build will be the best? And just to be part of the community that is discovering all of this is exciting. The messages on the floor will mean something again! Every wall will be tested, every jump will be made, every chest will be attacked, every phantom summoned, and every spirit broken. It will be glorious.
4.) Path of Exile is addicting!
Here, have a skilltree. No, seriously. Crazy, right?
I saw that Path of Exile was on Steam and free, so I decided to give it a go. I had played Diablo 2 in the best of all possible ways before: A pay by the hour computer bar. Those early years of the internet man, I tell ya. Eventually my brother and I split the cost of getting it on home, and played many, many characters throughout the years. I am a frugal gamer, so I haven’t picked up 3, but did try out the demo and liked what I saw.
Now, Path of Exile is actually pretty interesting. I have a character who regens something like 15 health per second, saps another 20 health per enemy hit, and deals 50 whenever he gets hit. Add in 50% dodge, 50% evasion, and 30% block, and I feel marginally invincible at the end of act 2! I am really interested to see how act 3 goes, and how the other classes are. Right now I’m running a tanky str/dex build, and really liking what I see. A lot of the mechanics are really well done compared to how I remember Diablo, but a few things are odd. No gold is one strange thing. Not earning actives by leveling is also very, very strange. But overall, it is a super cool game, and I have put in 10 hours since Thursday!
Did I mention that its free? All the microtransactions are cosmetic, so there is just pure, unadulterated, dungeon crawling in here. Next to TF2 and DOTA, this game is setting a hell of an example. Plus, the community is pretty great. I have found myself thinking that 'this chat room has a cool game attached to it'. DOWNLOAD IT! And create an FNF crew for it. I would, but...you know....effort.
5.) Deep Silver Loving
Deep Silver had its sale this weekend on Steam, so I was able to finally complete the PC trilogy of Saints Row games! I had been meaning to replay through each of them, but have been clearing out the other games from my backlog. But I have high hopes for Saints Row’s dick jokes, superpower fueled romp, along with visiting what made SR2 so special, and SR3 so mediocre.
I also picked up Risen 2 for a few dollars, on the recommendation from a cblog that I read the other week (sorry, forgot who!), which I am interested in. I also have had both Metro games in my backlog for a while as well, but I don’t think I can muster the courage to go through 2033 a second time, so I will probably just move over to Last Light first (when there’s time).
6.) Emo Games!
I have 2 games in my backlog that I have been looking forward to: Papa y Yo (which I have owned for about 2 months now) and To the Moon (about the same). I recently came off the high of Dear Esther for the first time, so I am interested to go through these games as well. Not to be too negative, but the narrator for The Stanley Parable just really didn’t do it for me in the demo that they had, so I don’t think I can jump in on that at least until there is another sale. I also have Little Inferno (which I hear gets good), and thomas was alone, but Ill be honest: those games are not for me. I think that its good that the games are hit and miss though, because at least people are trying something and not always landing on mediocre. I have heard a lot of love for those games, so they seem to be making a risk which is paying off, just not for me.
So, fellow dtoiders, whats got you riled up lately?